Stabilize as in everything is equal and nothing is too OP and everything that is has been relegated to Ubers? Well, there is no definite time as to when it will stabilize and it will be arguable if it is actually "stabilized". For example, Mike considers that the 5th Gen UU meta was completely perfect, despite maybe one or two Pokemon, however another user might feel it was too Offensively focused or Defensively, whatever they want to argue, but it won't be obvious as to when it is actually stabilized. Once everything that is over-powered is eliminated, that will be when the meta is "stable".
The average time is unpredictable and sometimes the Meta never stabilizes by the end of the generation. All we know is that every meta is unbalanced because Mega Banette is still allowed. o3o